Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q1 up to the prior quarter (i.e. 2018 Q1). The test period is a forecast for the current period and includes comparison to the appropriate median rent estimates for data observed so far in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic.

This page was last updated: 2018-06-05




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 303.5082 213.1803 206.3645 199.2351 199.3356
Training 324.2904 145.9141 145.9562 147.2658 146.1212



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 246.8036 151.3071 148.7606 142.0068 142.0296
Training 261.4572 100.9766 100.6866 102.2985 101.5110



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -230.4437 -872.8758 -871.7695 -874.5823 -875.7282



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -230.0655 -845.3892 -844.3364 -847.7891 -848.8186

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.4504 6.3451 82.3883 94.3203 107.3392 94.1694
Precision for idtract 30.7244 4.2509 23.1165 30.4724 39.8230 30.0119
Precision for idqtr 3704.6708 3774.0461 555.1018 2589.2781 13619.6753 1361.1160
Rho for idqtr 0.2605 0.3581 -0.4721 0.2856 0.8484 0.3946
Precision for idqtr1 14301.7423 17584.8007 273.1949 8209.2304 61744.3916 355.9311



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 93.8355 6.3360 81.9301 93.6445 106.8682 93.2967
Precision for idtract (iid component) 89.5317 21.5299 54.3300 87.1514 138.6177 82.6311
Precision for idtract (spatial component) 90.9134 29.1049 47.3318 86.4059 160.1996 78.1181
Precision for idqtr 4079.1123 4301.5361 601.1627 2800.3564 15333.9661 1461.4043
Rho for idqtr 0.2710 0.3539 -0.4606 0.2991 0.8472 0.4172
Precision for idqtr1 13100.1113 16510.2684 219.4255 7314.5731 57379.1514 254.5591



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.4707 6.3997 82.2951 94.3459 107.4481 94.2165
Precision for idtract (iid component) 88.4054 21.1967 54.4877 85.7736 137.1696 80.7179
Precision for idtract (spatial component) 90.3773 28.8205 47.1004 85.9687 158.9545 77.8441
Precision for idqtr 3554.0442 3622.3168 527.5372 2483.7992 13056.1822 1300.6018
Rho for idqtr 0.2736 0.3544 -0.4616 0.3025 0.8488 0.4245
Precision for idqtr1 14606.4354 17948.1158 292.0766 8429.1839 63163.9831 399.7527
Precision for idtractqtr 18790.0044 18391.5612 1351.3925 13401.4007 67326.8280 3739.1147

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)